Statements (25)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
gptkb:Harper's_equation
|
| gptkbp:application |
quantum mechanics
solid state physics quasiperiodic systems |
| gptkbp:field |
dynamical systems
mathematical analysis mathematical physics spectral theory |
| gptkbp:form |
ψ_{n+1} + ψ_{n-1} + 2λ cos(2πnα + θ)ψ_n = Eψ_n
|
| gptkbp:namedAfter |
Gustave Mathieu
|
| gptkbp:parameter |
α (alpha)
E (energy) θ (theta) λ (lambda) |
| gptkbp:property |
exhibits localization transition
has Cantor set spectrum for certain parameters |
| gptkbp:relatedTo |
gptkb:Hofstadter's_butterfly
Aubry–André model |
| gptkbp:studiedBy |
gptkb:Barry_Simon
Jean Bellissard Serge Aubry |
| gptkbp:bfsParent |
gptkb:Harper's_equation
|
| gptkbp:bfsLayer |
7
|
| https://www.w3.org/2000/01/rdf-schema#label |
almost Mathieu equation
|